Pallares and Hajjar

Journal of Constructional Steel Research 66 (2010) 198–212 

Contents lists available at ScienceDirect 

Journal of Constructional Steel Research 

journal homepage: www.elsevier.com/locate/jcsr 

Headed steel stud anchors in composite structures, Part I: Shear 

Luis Pallarés a , Jerome F. Hajjar b,∗ 

a Universidad Politécnica de Valencia, Valencia, 46022, Spain 

b Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2352, USA 

a r t i c l e i n f o 

Article history: 

Received 25 February 2009 

Accepted 18 August 2009 

Keywords: 

Composite construction 

Composite column 

Steel anchor 

Shear stud 

Headed stud 

Shear connector 

1. Introduction 

a b s t r a c t 

Headed steel stud anchors (shear connectors) welded to a steel 

base and encased in concrete have been the most common method 

for transferring forces between the steel and concrete materials 

in composite construction. This type of anchor has been investigated 

by numerous researchers worldwide. For steel and composite 

steel/concrete construction, the focus of the work has been 

predominantly on composite beams with and without a metal 

deck. Much less comprehensive assessment has been conducted 

for the strength of headed steel anchors in composite components. 

For such alternative configurations, the focus of much prior 

work has been on reinforced or prestressed concrete construction. 

The main approaches regarding anchors in reinforced concrete are 

outlined in [1] and Appendix D of ACI 318-08 [2]. Recently, Anderson 

and Meinheit [3–5] developed a comprehensive research program 

to assess the shear strength of headed studs in prestressed 

concrete. As a result of this work, the 6th Edition of the PCI Handbook 

[6] incorporated new alternative approaches for computing 

the shear strength of headed studs. 

∗ Corresponding author. Tel.: +1 217 244 4027; fax: +1 217 265 8040. 

E-mail address: jfhajjar@illinois.edu (J.F. Hajjar). 

0143-974X/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. 

doi:10.1016/j.jcsr.2009.08.009 

The formula in the 2005 American Institute of Steel Construction Specification to compute the strength of 

headed steel stud anchors (shear connectors) in composite steel/concrete structures has been used in the 

United States since 1993, after being proposed based primarily on the results of push-out tests. In the past 

several decades, the range of members used in composite structures has increased significantly, as has 

the number of tests in the literature on the monotonic and cyclic behavior of headed studs in composite 

construction. This paper reviews 391 monotonic and cyclic tests from the literature on experiments of 

headed stud anchors and proposes formulas for the limit states of steel failure and concrete failure of 

headed stud anchors subjected to shear force without the use of a metal deck. Detailing provisions to 

prevent premature pryout failure are also discussed. This paper also reviews proposals from several 

authors and provides recommended shear strength values for the seismic behavior of headed studs. The 

limit state formulas are proposed within the context of the 2005 AISC Specification, and comparisons are 

made to the provisions in the ACI 318-08 Building Code, the PCI Handbook, 6th Edition, and Eurocode 4. The 

scope of this research includes composite beam–columns [typically concrete-encased steel shapes (SRCs) 

or concrete-filled steel tubes (CFTs)], concrete-encased and concrete-filled beams, boundary elements of 

composite wall systems, composite connections, composite column base conditions, and related forms of 

composite construction. 

© 2009 Elsevier Ltd. All rights reserved. 

Research on headed studs in composite structures extends back 

to the 1950’s. A brief summary is presented here. The first push-out 

test for studying the behavior of headed studs was conducted by 

Viest [7], who performed 12 tests at the University of Illinois with 

varying ratios of effective depth-to-stud diameter (hef /d), where 

hef is the stud height from its base to the underside of the stud head. 

Viest [7] observed three types of failure: steel failures, where the 

stud diameter reached its yield point and failed; concrete failures, 

where the concrete surrounding the headed stud crushed; and 

mixed failures that included failure of both materials. Furthermore, 

Viest proposed one of the first formulas to assess the shear strength 

of headed studs of composite structures (see Table 1). 

Driscoll and Slutter [8] proposed a modification of Viest’s 

equation (Table 1) and observed that the total height-to-diameter 

ratio (h/d) for studs embedded in normal-weight concrete should 

be equal to or larger than 4.2 if the full shear strength of the anchor 

had to be developed. Chinn and Steele [9,10] developed push-out 

tests on lightweight composite slabs. Davies [11] studied group 

effects for several headed studs in push-out tests. Mainstone and 

Menzies [12] carried out tests on 83 push-out specimens covering 

the behavior of headed anchors under both static and fatigue 

loads. Goble [13] investigated the effects of flange thickness on 

the strength of composite specimens. Topkaya et al. [14] tested 

24 specimens in order to describe the behavior of headed studs at 

early concrete ages.

Notation 

As Area of the headed stud anchor 

Avg. (µ) Average 

Cv Coefficient for shear strengths 

C.O.V. Coefficient of variation 

Ec Modulus of elasticity of the concrete 

Ecm Secant modulus of elasticity of concrete 

d Diameter of the headed stud anchor 

f ′ 

c 

f 

Specified compressive strength of the concrete 

′ 

cr Average measured compressive strength of the 

concrete 

f ′ 

c,sp 

f 

Specified splitting tensile strength of concrete 

′ 

s 

Fu 

Yield stress of the steel 

Specified minimum tensile strength of a stud shear 

connector 

h Height of the stud 

hef Effective embedment depth anchor 

kcp Coefficient to compute pryout by ACI 318-08; it 

equals 1 for hef < 2.5 and 2 for hef ≥ 2.5 

Nb Nominal concrete breakout strength of a single 

anchor in tension in cracked concrete 

P Load applied in the test 

Qnv Nominal shear strength of anchor 

Qnvc Nominal shear strength in the concrete 

Qnvs Nominal shear strength in the steel 

Rg, Rp Metal deck coefficients in composite slabs 

Rm/Rn Average of the ratios between the test result and the 

predicted value 

St.D. (σ ) Standard deviation 

Vcp Concrete pryout strength of a single anchor in shear 

VR Coefficient of variation of resistance 

VF Coefficient of variation on fabrication 

VP Coefficient of variation of Rm/Rn 

VM Coefficient of variation of materials 

α Linearization approximation constant used to separate 

the resistance and demand uncertainties 

β Reliability index 

λ Modification factor for lightweight concrete 

ξ Reduction factor for cyclic loading 

φv Resistance factor for shear strength 

In the figures 

• Steel failure in test 

◦ Concrete failure in test 

× Mixed failure in test 

Ollgaard et al. [15] proposed the first formula adopted by the 

AISC Manual in 1993 to compute the shear strength of headed studs 

(see Table 1). They tested 48 push-out tests in lightweight and 

normal-weight concrete with an effective embedment depth ratio, 

hef /d, of 3.26. Failures were noted in both the steel and concrete 

material. 

Oehlers and Bradford [16] indicate that short studs experimentally 

show a lower shear strength than long steel stud anchors. The 

variation in the shear strength with height has been recognized 

in some national standards. For example, the British Standards for 

bridges (e.g., [17]) have given the strength of 19 × 100 mm steel 

stud anchors as 14%–18% stronger than 19 × 75 mm steel stud 

anchors depending on the strength of the concrete. Furthermore, 

[18], as a result of a finite element analysis, pointed out the rapid 

increase in strength with the height of the steel anchor. These authors 

noted that at a ratio of 7 between the height and the diam- 

L. Pallarés, J.F. Hajjar / Journal of Constructional Steel Research 66 (2010) 198–212 199 

Table 1 

Proposed equations for headed steel anchor strength in composite structures. 

Author Equation a 

Viest (1956) [7] If d < 1 in, then Qnv = 5.25d 2 f ′ 

� 

4000 

c f ′ 

c 

If d > 1 in, then Qnv = 5df ′ 

� 

4000 

c 

Driscoll and Slutter (1961) [8] Long studs (h/d > 4.2): Qnv = 932d2√f ′ 

c 

As 

Short studs (h/d < 4.2): Qnv = 222hd 

Buttry (1965), Baldwin et al. 

√ 

f 

′ 

c 

As 

Steel failure: Qnvs = Asf ′ 

(1965), Dallam (1968) [22–24] 

s 

Concrete failure: 

Qnvc = 0.0157hdf ′ 

Ollgaard et al. (1971) [15] 

c,sp + 6.80 

� 

Qnvs = 0.5As f ′ 

c 

Ec < AsFu 

a Units: pounds, inches for [7]; Units: kips, inches for [8,23,22,24,15]. 

eter of the shank, the strength is 98% of the maximum attainable 

strength. 

The AISC Specification has included provisions for composite 

structures since 1936. Tables providing allowable horizontal shear 

load of headed studs as a function of the stud diameter and 

concrete strength appeared in the AISC Specification of 1961 

[19]. The effects of a metal deck on the shear strength of the 

headed studs were added in 1978 [20] and the AISC Specification 

adopted Ollgaard’s formula [15] to compute the shear strength of 

headed steel studs in 1993 [21]. In Europe, codifying provisions 

for composite construction as part of Eurocode (EC) culminated 

with an initial version of the provisions being issued in the 1990’s, 

followed by issuing of Eurocode-4 (2004) more recently. 

Composite beams, specifically hot-rolled steel shapes with a 

concrete floor slab either with or without metal deck formwork, 

have received extensive coverage in the literature (e.g., [8,22–29]) 

and are not within the scope of this paper. 

This paper reviews 391 monotonic and cyclic tests from the 

literature on experiments of headed stud anchors and proposes 

formulas for the limit states of steel failure and concrete failure 

of headed stud anchors subjected to shear force without the use 

of a metal deck. Detailing provisions to prevent premature pryout 

failure are also discussed. This paper also reviews proposals 

from several authors and provides recommended shear strength 

values for the cyclic seismic behavior of headed studs. The limit 

state formulas are proposed within the context of the AISC Specification 

[30,31] and EC-4 (2004) [32], and comparisons are made to 

the provisions in the ACI 318-08 Building Code [2] and the PCI Handbook, 

6th Edition [6]. The scope of this research includes composite 

beam–columns [typically concrete-encased steel shapes (SRCs) or 

concrete-filled steel tubes (CFTs)], concrete-encased and concretefilled 

beams, boundary elements of composite wall systems, composite 

connections, composite column base conditions, and related 

forms of composite construction. Pallarés and Hajjar [33] cover the 

response of steel stud anchors subjected to tension force and combined 

tension and shear. 

This paper also reviews cyclic tests under high-amplitude 

loading simulating seismic excitation. Hawkins and Mitchell [34], 

Gattesco and Giuriani [35], Bursi and Gramola [36], Zandonini 

and Bursi [37], and Civjan and Singh [38] performed a range of 

different types of push–pull tests on headed steel studs under 

high amplitude cyclic shear loading for slabs in composite beams. 

Saari et al. [39] reported the headed stud anchor behavior of 

partially-restrained steel frames with reinforced concrete infill 

walls, looking at both static and cyclic loads. Saari et al. [39] studied 

shear, tension, and shear/tension interaction response for headed 

studs with two types of confining reinforcing patterns. These tests 

showed that if sufficient confinement is included, concrete failure 

is precluded. 

2. Objectives 

This paper reports on the behavior of headed studs embedded 

in solid concrete slabs subjected to shear force, including both 

f ′ 

c

200 L. Pallarés, J.F. Hajjar / Journal of Constructional Steel Research 66 (2010) 198–212 

static and large-amplitude cyclic (i.e., seismic) forces, without 

steel profile sheeting or a metal deck. The results given in 

this work are applicable to composite elements including steel 

reinforced concrete columns (SRCs) or concrete-filled tubes 

(CFTs), concrete-encased and concrete-filled beams, boundary 

elements of composite wall systems, composite connections, 

composite column base conditions, and related forms of composite 

construction. In this work, the limit states of failure in the steel 

anchor and concrete pryout are accounted for in the assessments 

made and the recommendations put forward. As discussed below, 

the limit state of concrete breakout, as defined for stud anchors in 

shear in ACI 318 Appendix D [2], is assumed not to be a governing 

limit state for these forms of composite construction. An extensive 

set of test results of headed steel anchors in configurations 

applicable to composite construction has been collected and 

analyzed relative to the design provisions put forward in AISC 

[30], EC-4 (2004) [32], ACI 318-08 Appendix D [2], and PCI 6th 

Edition (PCI, 2004) [6]. Recommendations and design guidelines 

are then proposed for headed steel anchors subjected to shear force 

in composite construction. Approximately 27% of the test results 

utilized in this work include lightweight concrete so as to get a 

comprehensive set of test results for composite construction. 

3. Monotonic behavior of headed studs subjected to shear 

forces 

A comprehensive collection of headed steel anchors tests under 

static loads may be found in [4]. The present work is based mainly 

on that collection with added test data found in the literature, 

including [40,41,12,42,39,43]. In total, 391 tests were considered 

when examining the monotonic behavior of headed steel anchors. 

There are three main failures that may occur in a headed stud 

anchor for composite structures, namely: steel failure, weld failure, 

and failure of the concrete surrounding the headed stud. In this 

work, weld failure is included as a steel failure, since the distinction 

between weld and steel failure is often difficult to ascertain in the 

experiments. 

Of the 391 tests on headed steel studs, 114 tests were classified 

as concrete failure and 202 were classified as steel failure. The rest 

of the failures were not reported by the author or were classified as 

mixed failure. Within this data set, 286 tests used normal-weight 

concrete and 105 of the tests used lightweight concrete. 

Schematics of the tests are presented in Table 2. Generally, 

there are three types of tests. The first type is a push-out test 

[e.g., [7,15], etc.]. The second type is conducted horizontally with 

edge conditions far away from the tested steel anchor [e.g., [4,35]]. 

The third type takes into account special conditions such as in 

infill walls (e.g., [39]). The push-out test usually simulates well 

the conditions in composite structures, producing pryout or steel 

failure of the anchor between the steel and concrete. 

The collected tests have been used to assess the approaches 

proposed by AISC [30], EC-4 (2004) [32], PCI 6th Edition [6], and 

ACI 318-08 [2]. All four of the provisions use a general form 

of φvCvAsFun to predict the strength of the headed stud when 

the failure occurs in the steel shank, where φv is the resistance 

factor, Cv is a reduction factor of the strength, As is the crosssectional 

area of the headed stud and Fu is the specified (nominal) 

minimum tensile strength of the headed stud anchor, and n is the 

number of studs. The coefficient values from the three standards 

are presented in Table 3. 

The general form of the formulas to compute the nominal 

strength of an individual headed stud anchor when failure is in 

the concrete, as provided by ACI 318-08 [2] and PCI 6th Edition 

[6], is φvCvRvn. These formulas are based on the 5% fractile; that 

is, the formulas are developed such that there is a 90% confidence 

level that over 95% of the failures occur above the calculated limit 

state value for an individual anchor [48]. The ACI 318-08 average 

strength formulas are given in [49]. The PCI 6th Edition average 

strength formulas are given in [4]. 

The most likely concrete failure modes that may occur in composite 

construction given by ACI 318-08 Appendix D are breakout 

and pryout. Breakout is a type of failure occurring when free edge 

conditions govern the failure. In these cases, failure planes form a 

volume of concrete surrounding the anchor, separating this concrete 

from the member. In contrast, pryout failure happens in a local 

area surrounding the anchor corresponding to a formation of a 

concrete spall in the direction perpendicular to the applied shear 

force. It is likely that breakout failure rarely occurs in composite 

structures and is assumed in this work not to be a governing limit 

state since there are not appropriate failure planes for front-edge 

or side-edge breakout in the vast majority of composite members, 

particularly if typical reinforcement detailing is used. The tests reported 

by Ollgaard et al. [15] are representative of the fact that 

pryout, following the terminology of ACI 318-08, or ‘‘in the field’’ 

following the terminology of PCI 6th Edition, is the concrete failure 

mode that is most likely to occur in composite structures. 

ACI 318-08 proposes a formula to compute the pryout failure 

(Vcp) based on the basic concrete breakout strength in tension 

(Nb), which necessitates the computation of several intermediate 

quantities. However, PCI 6th Edition provides a direct formula to 

compute the pryout failure when the ratio hef /d is less than 4.5. 

This assumes that when the ratio hef /d is larger than 4.5, the most 

likely failure is in the steel shank. The formulas from ACI 318-08 

and PCI 6th Edition to compute the pryout failure are summarized 

in Table 3. 

AISC [30] provides a formula to compute the shear strength in 

composite components other than composite beams. This formula 

is an adaptation of the formula for headed steel anchors in 

composite beams proposed by Ollgaard et al. [15], who calibrated 

it by adjusting different models to the 48 test results developed 

in their research. Currently, reliability of the headed steel anchor 

against premature failure is taken into account as a part of the 

design of the composite component, such as a composite column; 

hence, the headed steel anchor strength typically does not have its 

own resistance factor in AISC [30]. The resulting formula (Equation 

I2-12 in [30]) is presented in Table 1 (as [15]). Eurocode-4 (2004), in 

contrast, proposes a similar formula to compute the shear strength 

in composite members, but this formula is affected by partial safety 

factors (Table 3) that provide more conservative results than [30]. 

4. Comparison of AISC 2005, EC-4, ACI 318-08, AND PCI 6th 

Edition 

The current formula for the nominal shear strength of a 

steel anchor � (other than in composite �beams) in AISC [30] 

(0.5As f ′ 

c 

Ec < AsFu) and EC-4 [32] (Cv0.5As f ′ 

c 

Ecm) was computed 

for each of the 391 tests (using the minimum value of the steel 

and concrete failure modes) and compared to the experimentally 

obtained load. In these formulas, measured values of Ec are used, or 

in cases where the measured values are not provide, Ec is calculated 

per ACI 318-08 [2] using measured properties of the concrete 

strength. Ecm is calculated per [50] using measured properties of 

the concrete strength. Measured Fu values were not provided by 

the authors in a very small number of cases. In these cases, for this 

study, the specified (nominal) values of Fu given by the authors 

were used. 

The results are shown in Fig. 1(a, e). 1 The ratio of experimental 

strength to predicted strength, Vtest/Vpredicted, was less than 1 for 

235 of the 391 tests for AISC 2005, indicating that the formula is 

1 The legend for the markers in the figures is identified in the list of notation.

Table 2 

Headed steel anchor test configurations. 

Reference hef /d # 

Tests 

Viest (1956) [7] 

Shoup and Singleton (1963) [40] 

Chapman and Balakrishnan 

(1964) [41] 

Buttry (1965) [22] 

Chinn (1965) [9] 

Mainstone and Menzies (1967) 

[12] 


2.47, 2.55, 3.23, 3.22, 4.53, 

4.67, 4.77, 5.50, 7.00 

8.00, 6.30, 5.20, 6.67, 9.33, 

9.65 

12 1 

Type Type of test Type of concrete Range of f ′ 

c ksi (MPa) 

4 studs (2 per side) Normal: 12 tests 3.19–4.39 

8 studs (4 per side) Lightweight: 0 tests (22.0–30.2) 

9 2 8 studs (4 per side) 

2, 3.29, 4.67, 7.29 9 1 4 studs (2 per side) 

2.00, 3.33, 3.50, 4.67, 5.38, 

5.90, 7.38 

3.33, 3.38, 3.41, 4.00, 4.67, 

5.38, 4.67 



4.67 11 1 4 studs (2 per side) 

Davies (1967) [11] 4.67 19 

Steele (1967) [10] 3.50 18 1 4 studs (2 per side) 

Dallam (1968) [24] 4.00, 4.67, 5.90, 7.38 17 1 4 studs (2 per side) 

Baldwin (1970) [25] 3.50, 4.00, 4.67, 5.90, 7.38 26 1 4 studs (2 per side) 

Menzies (1971) [42] 4.67 6 1 4 studs (2 per side) 

Hawkins (1971) [44] 

2.00, 2.33, 2.86, 3.00, 3.51, 

4.00, 4.67 

22 2 

1, 2, 

3 

Ollgaard et al. (1971) [15] 3.50, 4.21 48 1, 2 

Klingner and Mendonca (1982) 

[45] 

Hawkins and Mitchell (1984) 

[34] 

11 8 5 ‘‘In the field’’ 

3.33 2 5 ‘‘In the field’’ 

Jayas and Hosain (1989) [26] 4.30 1 3 12 studs (6 per side) 

Zhao (1993) [46] 2.27, 2.96, 4.09 18 5 ‘‘In the field’’ 

An and Cederwall (1996) [47] 3.51 8 2 8 studs (2 per side) 

Gattesco et al. (1996) [35] 6.58 1 5 ‘‘In the field’’ 

Saari et al. (2004) [39] 6.67 2 4 4 studs (2 per side) 

Shim et al. (2004) [43] 5.68, 5.22, 4.70 17 2 8 studs (4 per side) 

Anderson and Meinheit (2005) 

[4] 

3.62, 4.21, 4.81, 5.32, 5.93, 

9.84 

unsafe for 60% of the tests. The results for EC-4 (2004) are more 

conservative, since 309 of the 391 tests resulted in ratios less than 

1, indicating that the formula is unsafe for 21% of the tests. 

105 5 ‘‘In the field’’ 

Normal: 9 tests 3.43–4.89 

Lightweight: 0 tests (23.6–33.7) 

Normal:9 tests 3.64–6.10 








4, 6, or 8 studs Normal:19 tests 3.76–5.52 

(2, 3, or 4 per side) Lightweight: 0 tests (25.9–38.0) 









4 studs (2 per side) Normal:22 tests 2.89–5.04 


4 studs (2 per side) Normal:18 tests 2.67–5.08 


Normal:8 tests 4.28 

Lightweight: 0 tests (29.5) 

Normal:2tests 1.97–8.98 


Normal:1tests 4.37 






Normal:1 tests 3.77 








Additional insight can be gained by separating the tests 

based on the failure mode before computing the average testto-predicted 

ratio. For steel failures, the AISC 2005 prediction is


Table 3 

Steel and concrete strength by AISC, PCI 6th Edition, and ACI 318-08. 

Steel failure 

φQnvs = φvCvAsFun 

Concrete failure (pryout, or ‘‘in the field’’) φQnvc = φvCvRvn 

φv Cv φvCv φv Cv φvCv Rv b 

Average formula 5% fractile 

� 

AISC 1.00 1.00 1.00 1.00 1.00 1.00 0.5As f ′ 

c 

Ec 

� 

EC-4 

0.66 0.48 0.5As f ′ 

0.80 0.80 0.64 0.80 

c 

Ecm 

PCI 6th 1.00 0.75 0.75 0.70 1.00 0.70 317.9λ � f ′ 

c (d)1.5 � �0.5 hef 

ACI 318-08 a 

Ductile steel element 0.65 1.00 0.65 

0.70 1.00 0.70 kcp40λ � f ′ 

Brittle steel element 0.60 1.00 0.60 

� �1.5 c 

hef 

a The formulas for a ductile headed steel anchor have been used in this work. 

b Units: pounds, inches for ACI 318-08 and PCI 6th Edition; Units: kips, inches for AISC. N, mm for EC-4. 

c The Cv factor depends on the height of the stud. 

Table 4 

Test-to-predicted ratios for steel failure in tests using the minimum strength provided by the standards. 

Shear forces 202 tests Without resistance factor With resistance factor 

0.74 c 

0.60 

215λ � f ′ 

c (d)1.5 � �0.5 hef 

kcp24λ � f ′ 

� �1.5 c 

hef 

AISC EC-4 ACI 318-08 PCI 6th AISC EC-4 ACI 318-08 PCI 6th 

Average 0.986 1.215 1.150/1.344 a 

Stand. dev. 0.158 0.195 0.560/0.815 a 

a γ 1/γ 2 : γ 1: uses the average value; γ 2: uses the 5% fractile formula. 

1.051/1.498 a 

0.183/0.311 a 

Table 5 

Test-to-predicted ratios for concrete failure in tests using the minimum strength provided by the standards. 

Shear forces 114 tests Without resistance factor With resistance factor 

0.986 1.518 1.974 2.142 

0.158 0.244 1.141 0.441 

AISC EC-4 ACI 318-08 PCI 6th AISC EC-4 ACI 318-08 PCI 6th 

Average 0.849 0.996 1.576/2.097 a 

St. dev. 0.244 0.245 0.766/1.026 a 

a γ 1/γ 2: γ 1: uses the average value; γ 2: uses the 5% fractile formula. 

accurate and safe (Fig. 1(b)), with EC-4 showing more conservative 

results due to the 0.8 reduction factor (Fig. 1(f)). For tests in which 

the concrete failed, the scatter is much larger and many test-topredicted 

ratios are less than 1 (Fig. 1(c)) for AISC 2005; EC-4 again 

presents a more conservative range of results (Fig. 1(g)). 

The comparison between the different provisions for concrete 

failure modes has been carried out using the average formula, the 

5% fractile formula provided by ACI 318-08 and PCI 6th Edition, and 

taking into account the resistance factors specified in Table 3, in 

order to assess the accuracy of the different approaches. The testto-predicted 

ratios for ACI 318-08 Appendix D and PCI 6th Edition 

are shown in Fig. 2. The headed stud strength plotted in Fig. 2 is 

the minimum of the strength of the steel (AsFu) and the strength 

computed for pryout (‘‘in the field’’) failure mode. 

Based on using the average formula for predicting stud strength 

in shear, it can be seen that PCI 6th Edition (Fig. 2(b)) is more 

accurate than ACI 318-08 Appendix D (Fig. 2(a)) in predicting the 

local failure of the concrete surrounding stud, and its standard 

deviation shows less scattered results. ACI 318-08 is more 

conservative than PCI 6th Edition due primarily to the auxiliary 

coefficient kcp equaling 1 in ACI 318-08 when the headed stud 

is less than 2.5 in (63 mm), as pointed out by Anderson and 

Meinheit [4]. AISC has lower average ratios than ACI 318-08 and PCI 

6th Edition, and the scatter is larger, with a considerable number 

of tests (approximately 60%) having a test-to-predicted ratio less 

than 1.0 (Fig. 1(a)). 

The results derived from applying 5% fractile formulas for 

pryout strength given by ACI 318-08 and PCI 6th Edition are shown 

in Fig. 2(c) and (d). The scatter of the results applying the 5% fractile 

formulas, both with and without resistance factors (Fig. 2(e) and 

(f)) is larger than results given by average values (Fig. 2(a) and (b)), 

and ACI 318-08 provides more conservative results in comparison 

to PCI 6th Edition. The differences between [30], ACI 318-08 and 

1.011/1.495 a 

0.168/0.249 a 

0.849 1.245 2.997 2.127 

0.244 0.307 1.465 0.363 

PCI 6th Edition also typically become larger when the respective 

resistance factors are applied. 

The formulas used for stud strength in shear in AISC and EC- 

4 were derived by looking at all tests in aggregate, regardless of 

the mode of failure. It is informative to compare the accuracy of 

the various formulas for predicting the steel or concrete failure 

modes by comparing each formula only to tests failing in the steel 

or concrete, respectively. If only tests that failed in the steel are 

examined (202 tests), EC-4 provides the most conservative results 

(Table 4). PCI 6th Edition provides the most conservative results 

when using the 5% fractile equation or when resistance factors are 

applied. Similarly, for headed stud anchors failing in the concrete 

(114 tests), ACI 318-08 is shown to be the most conservative, while 

PCI 6th Edition is accurate with small scatter (Table 5). AISC is seen 

to be unsafe for both groups of tests. 

The strength prediction (AsFu) for steel failure (202 tests) may 

be seen in Fig. 3. This formula becomes more conservative when 

the specified (nominal) values of the steel strength are used rather 

than measured values. 

Fig. 4 shows the results of using concrete failures to assess 

tests that failed in the concrete. It can be seen that PCI 6th Edition 

is more accurate than ACI 318-08 Appendix D, although PCI 6th 

Edition restricted its proposed formula for ‘‘in the field’’ cases, or 

pryout, for headed studs with the ratio hef /d < 4.5. ACI 318- 

08 Appendix D again provides very conservative results when the 

effective height of the stud is less than 2.5 in (63 mm), due to the 

kcp coefficient, as discussed earlier. If the AISC formula for concrete 

failure is used similarly, the results are less conservative, especially 

without resistance factors (Fig. 1(c)). For EC-4, the average result is 

conservative (Fig. 1(g)).


Fig. 1. Assessment of anchor strength using the minimum of steel and concrete failure formulas in AISC and EC-4. 

5. Reassessment of headed steel stud strength in the AISC 

specification 

From Fig. 3 and Table 7, where the steel formula and concrete 

formula of EC-4 with resistance factors are assessed respectively, 

it is seen that EC-4 presents conservative results for design purposes, 

particularly when the resistance factor is applied, For AISC 

[30], the results are less conservative; as a result, new resistance 

factors are assessed in this paper for these provisions based on use 

of the experimental database. Using recommendations by Ravindra 

and Galambos [51], resistance factors can be computed to compensate 

for the scatter and low mean values exhibited by the results 

from the current AISC [30] formulas, as seen in Fig. 1. Given a reliability 

index, β, the resistance factor can be computed using Eq. (1). 

φ = Rm 

e (−αβVR) , (1) 

Rn 

where 

Rm is the average of the ratio between the test result and the 

Rn 

predicted value;


Fig. 2. Assessment of anchor strength using the minimum of steel and concrete failure formulas in [2] Appendix D and [6]. 

α is equal to 0.55, given by Ravindra and Galambos [51]; 

β is the reliability index; and 

VR = 

� 

V 2 

F 

+ V 2 

P 

+ V 2 

M , where VF is the coefficient of varia- 

tion on fabrication and is taken as VF = 0.05 as recommended 

by Ravindra and Galambos [51], reflecting the strong control characteristics 

of stud manufacturing; VP is the coefficient of variation 

of Rm 

Rn ; VM is the coefficient of the variation of the materials and is 

taken as VM = 0.09 based on test data from [52–54]. 

Ravindra and Galambos [51] recommend a reliability index β 

of 3 for members and 4.5 for connections. In this work, a reliability 

index of 4 has been targeted to compute the resistance factors. 

Resistance factors for steel strength prediction using only tests 

that failed in the steel are computed for values of the Cv coefficient 

equal to 1.00, 0.75 and 0.65 (Table 6). Values of the resistance factor 

for a β value of both 3 and 4 are presented. Eq. (2) presents a sample 

calculation for Cv = 1.00 and β = 4. 

φv = Rm 

e 

Rn 

(−0.55βVR) (−0.55·4.0·0.160) 

= 0.933e = 0.65. (2) 

With Cv = 0.65 the resistance factor computed by Eq. (2) is larger 

than 1.0, so it should be taken as 1.0. 

Table 6 

Resistance factors computed for CvAsFy for Cv = 1, Cv = 0.75 and Cv = 0.65 for 

steel strength based on steel failure in tests. 

202 tests Cv µ σ C.O.V. φ 

β = 3 β = 4 

S1 1.00 0.933 a 

S2 0.75 1.224 a 

S3 0.65 1.436 a 

0.150 0.161 0.68 0.61 

0.200 0.161 0.89 0.80 

0.231 0.161 – 0.94 

a With measured values reported by authors or nominal values if the measured 

steel strength was not reported. 

6. Formulas for concrete failure 

The concrete failure formulas of ACI 318-08 and PCI 6th Edition 

are geared for general conditions for preventing failure of headed 

steel anchors, especially cases where free edges may be close to 

the stud. Such free edges rarely occur in composite construction. 

Thus, several alternative formulas were developed in this work 

to compute the concrete strength surrounding headed studs for 

conditions commensurate with composite construction. These 

formulas are compared with the AISC and EC-4 formulas in Table 7. 

It can be seen that the mean value of the test-to-predicted ratios for 

the AISC formula in particular is quite low, coupled with a relatively 

large coefficient of variation. Both the optimized formula and

simplified versions of these formulas are shown. The equations are 

functions of the properties of the headed steel anchors, including 

height, shank diameter, and concrete strength. The proposed 

formulas have been calibrated using a least squares technique, 

constraining the average test-to-predicted ratio to equal 1.0 for 

all 114 tests failing in the concrete (Fig. 5). The statistical values 

for optimized formulas and then their corresponding simplified 

formulas developed to predict concrete failures of anchors loaded 

in shear in composite construction are shown in Table 7. 

Proposals 1 and 2 have the same form as the current formula 

of AISC and EC-4, without distinguishing the concrete weight. 

Proposal 3 takes into account the stud height, similar to PCI 

6th Edition and ACI 318-08. Proposal 4 takes into account 

the concrete weight (λ), with the result being similar to one 

�proposed by Anderson and Meinheit [4]. The coefficient λ = 

f 

′ 

� 

1 

≤ 1.0 (in psi) or λ = 

≤ 1.0 

c,sp 

6.7 

� 1 

√f ′ 

c 


Fig. 3. Steel failure formulas in comparison with steel failure in tests. 

� f ′ 

c,sp 

0.046 

√ 

f 

′ 

c /0.0069 

(in MPa) is a lightweight concrete factor. It can be computed 

following either ACI 318-08 or PCI 6th Edition. If the value 

of the splitting tensile strength f ′ 

c,sp is not known, λ equals 

0.85 for sand–lightweight concrete and 0.75 for all-lightweight 

concrete. Lightweight concrete according to ACI 318-08 is concrete 

containing lightweight aggregate and having a density between 

90 lb/ft 3 (1440 kg/m 3 ) and 115 lb/ft 3 (1840 kg/m 3 ). 

Table 7 shows the resistance factors (φ) for reliability indices 

of 3 and 4 for the tests that failed by the concrete. It can be 

seen that all four proposals result in similar resistance factors, 

equaling approximately 0.60 for a reliability index of 4 and 0.70 

for a reliability index of 3. 

7. Headed steel stud shear strength for hef /d > 4.5 

From the earliest tests carried out by Viest [7], it has been seen 

that hef /d is a significant parameter that often delineates the type 

of failure that occurs in tests that do not have free edge conditions. 

In the tests by Viest [7], for example, the failure normally occurred 

in the steel stud when hef /d was larger than 4.53. Driscoll and 

Slutter [8] observed that, if h/d was greater than 4.2, they could 

develop all the strength in tension (i.e., AsFu) rather than shear, and 

the tensile strength then determined the ultimate strength of the 

studs in their push-out tests. It was further noted that, for studs 

shorter than h/d = 4.2, the strength must be reduced because of 

the possibility of the ultimate strength being reduced by fracture 

of the concrete. Ollgaard et al. [15] tested studs with an effective 

embedment depth of 3.50 and 4.20. They indicated that in many 

tests both steel and concrete failures were observed in the same 

specimen. 

A summary of failures found in the tests in the database 

classified as having studs that are greater than or less than a given 

hef /d ratio (including ratios of 4.00, 4.50, 5.50, and 6.50) is given 

in Table 8. AISC [30] states that headed steel studs shall not be 

less than four stud diameters in length after installation and EC- 

4 applies a reduction factor on the stud strength for ratios of h/d 

between 3 and 4. Recognizing the h/d limitation in AISC [30] and 

assuming that h is a few percent larger than hef to account for the 

depth of the stud head, it can be reasoned that for a headed stud 

whose h/d value is right at the limit, approximately 73% of the 

failures are likely to occur in the steel. In contrast, 81% of the tests 

having a ratio hef /d larger than 4.50 failed in the steel, and 91% 

failed in the steel for hef /d larger than 5.50. 

Based on these results, if the minimum h/d ratio limit of 4 in 

AISC [30] is recommended for increase to 5 (i.e., hef /d equaling 

4.5 for a 3/4 in (19 mm) diameter headed stud having a 3/8 

in (9.5 mm) depth of the head), 81% of the 224 tests with ratios 

larger than this limit failed in the steel. In order to predict the 

failure of the remaining 19% of the tests that failed in the concrete, 

one of the proposed formulas in the prior section could be used, 

taking the minimum value of steel and concrete failures. However, 

as discussed below, checking the steel formula alone may be 

adequate for this minimum ratio of hef /d. 

The required resistance factor for headed studs with hef /d ratios 

larger than 4 and 4.5 is presented in Table 9. Fig. 5 then plots the 

test-to-predicted ratios, separating tests based on their value of 

hef /d. Also, in these plots, both the measured material strengths


(Fig. 5a, b, g) and the specified (nominal) material strengths (Fig. 5c, 

d, e, f) are used in the formulas for both steel and concrete 

failures so as to provide an indication of the test-to-predicted 

values using nominal values typical in design calculations. AWS 

D1.1/D1.1:2006 Structural Welding Code—Steel [55] specifies two 

types of headed stud, type A and type B, for use in composite 

systems depending on their function within the structure. The 

main difference between them is the ultimate tensile strength of 

the headed stud. Type A [Fu = 61 ksi (420 MPa)] are generalpurpose 

headed studs of any type and size used for purposes other 

than shear transfer in composite beam design and construction. 

Type B [Fu = 65 ksi (450 MPa)] are studs that are headed, bent, 

or of other configuration, with diameter of 3/8 in (9.5 mm), 1/2 

in (12.5 mm), 5/8 in (16 mm), 3/4 in (19 mm), 7/8 in (22 mm) or 1 

in (25 mm), and that are used commonly in composite beam design 

and construction. The AISC [30] commentary provides steel anchor 

material specifications that include specified (nominal) yield and 

tensile strengths of typical ASTM A108 [56] Type B studs as 51 ksi 

(350 MPa) and 65 ksi (450 MPa), respectively (AWS 2004). 

ACI 301-08 [57] provides formulas for the average measured 

concrete (f ′ 

cr ) strength given the specified (nominal) concrete 

strength (f ′ 

′ ′ 

c ); for example, f cr = f c + 1200 (in psi), for a 

specified (nominal) concrete strength between 3000 and 5000 psi. 

In Fig. 5, the stud strength has then been computed using the 

Fig. 4. Concrete failure formulas in comparison with concrete failure in tests. 

specified concrete strength derived from the average measured 

concrete strength reported in the test. An important conclusion 

from this figure is that if hef /d is restricted to being larger than 

4.5 (or, comparably, h/d is restricted to being larger than 5), using 

the steel formula alone is adequate to safely predict the shear 

strengths of the studs. Even those tests that fail in the concrete are 

generally seen to have test-to-predicted ratios larger than 1, with 

little difference from the case where both the steel and concrete 

formulas are checked, and the minimum used (as seen in Fig. 5(d) 

and (f)). In Fig. 5(c) and (e), using only the steel formula with 

specified (nominal) strength values results in test-to-predicted 

ratios of 1.964 for studs with Fu of 51 ksi (350 MPa) and 1.541 for 

studs with Fu of 65 ksi (450 MPa), based on using 0.65AsFu as the 

design strength of the headed stud failing in shear. 

Fig. 6 plots the test-to-predicted ratios for all tests using the 

minimum of the steel strength (0.65AsFu) and concrete strength 

formulas for several different concrete strength formulas. The 

figure compares steel (•) and concrete (×) formula predictions, 

distinguishing type of failure in the top of each figure (C.F. means 

concrete failure, M.F. means mixed failure, and no mark means 

steel failure). It may be seen that the concrete formula always 

controls the strength prediction for hef /d < 4.5, which is 

commensurate with the type of failure (concrete failure or mixed 

failure) found in most of those tests. In contrast, the concrete


Fig. 5. Test-to-predicted values using only the steel formula (a, c, e, g) or the minimum of the steel and concrete formulas (b, d, f).


Table 7 

Evaluation of concrete formulas for headed stud anchors in shear from AISC 2005, EC-4, and proposed concrete formulas. 

Formula for Qnvc a µ σ C.O.V. φ 

β = 3 β = 4 

AISC 2005 

EC-4 

� 

0.5As f ′ 

c 

Ec 

Cv0.5 

0.827 0.250 0.302 0.49 0.41 

� f ′ 

c Ecm 0.965 0.249 0.258 0.61 0.52 

Proposal 1 17.000As 

17As 

� � 

′ 0.452 

f c (Ec) 0.041 

� � 

′ 0.45 

f c (Ec) 0.04 

� � 

′ 0.209 

Proposal 2 6.214As f c 

Ec 

� � 

′ 0.2 

6.2As f c 

Ec 

Proposal 3 18.197As 

18As 

� � 

′ 0.479 0.215 

f c (h) 

� � 

′ 0.5 0.2 

f c (h) 

Proposal 4 8.915λ � f ′ 

�0.476 1.373 0.564 

c (d) (h) 

9λ � f ′ 

�0.5 1.4 0.6 

c (d) (h) 

a Optimized formula/Simplified formula. Units: kips, inches. 

formulas of Proposals 1–3 (Fig. 6(a)–(c)) incorrectly control for 

hef /d > 4.5, even though steel failure often occurs in those tests. 

In Proposal 4 (Fig. 6(d)) (which is similar to the concrete formula 

of PCI 6th Edition) and in ACI 318-08 (Fig. 6(e)), prediction of 

the type of failure typically matches better with the actual failure 

mode. However, the results of using the minimum of the steel 

and concrete formulas tend to be unnecessarily conservative for 

hef /d > 4.5, and the prediction may be reasonable based upon 

1.001 0.242 0.242 0.65 0.56 

1.013 0.245 0.242 0.66 0.57 

1.002 0.242 0.242 0.65 0.56 

1.098 0.265 0.242 0.71 0.62 

0.999 0.237 0.237 0.65 0.57 

0.997 0.237 0.237 0.65 0.57 

1.021 0.219 0.214 0.69 0.61 

0.955 0.206 0.216 0.64 0.56 

checking only the steel formula, as mentioned above, due to the 

limited cases with concrete or mixed failures and the reasonable 

predictions made for those specific cases using the steel formula. 

While Table 9 and Figs. 5 and 6 include tests with both 

normal-weight and lightweight concrete, to be conservative, all 

of the recommendations discussed so far in this section could be 

limited to the use of normal-weight concrete. This is because for 

lightweight concrete, 35% of the tests have hef /d > 4.5, whereas

Table 8 

Summary of test failure for several hef /d ratios. 

All tests 


# tests S.F. a 

C.F. b 

M.F. c 

Comments 

hef /d ≥ 4.00 251 184 51 16 73.33% failed in the steel 

hef /d < 4.00 140 18 63 54 87.14% failed in the concrete or mixed failure 







Normal-weight concrete 









Lightweight concrete 







hef /d ≥ 6.50 10 10 0 0 100% failed in the steel 


a S.F.: Steel failure (weld failures are included as steel failures). 

b C.F.: Concrete failure. 

c M.F.: Mixed failure or not reported. 

Table 9 

Resistance factors for tests with hef /d ratios larger than 4.5 and 4.0. 

224 tests, hef /d > 4.5 φ 251 tests, hef /d > 4.0 φ 

Cv µ σ C.O.V. β = 3 β = 4 Cv µ σ C.O.V. β = 3 β = 4 

Option 1 1.00 0.910 0.158 0.174 0.65 0.58 1.00 0.890 0.172 0.193 0.62 0.55 

Option 2 0.75 1.213 0.211 0.174 0.87 0.77 0.75 1.186 0.229 0.193 0.83 0.73 

Option 3 0.65 1.399 0.244 0.174 – 0.90 0.65 1.369 0.264 0.193 0.95 0.85 

for normal-weight concrete 65% of the tests have hef /d > 4.5, 

thus providing a much larger sample size (see the portions of 

Table 8 that disaggregate the test data for different weights of 

concrete). Thus, it may be deemed less conclusive what value of 

hef /d is required to ensure that just checking a steel failure formula 

is adequate for lightweight concrete. The results of Fig. 5 imply 

that the steel strength formula adequately predicts both normalweight 

and lightweight concrete failures, but Table 8 shows that a 

relatively large percentage of failures are occurring in the concrete 

if a minimum value of hef /d is taken as 4.5. From Table 8, a value of 

6.5 for hef /d (i.e., or a value of h/d > 7) more clearly assures failure 

in the steel for lightweight concrete, and thus this is proposed as 

the minimum hef /d for lightweight concrete if only the steel failure 

mode is to be checked. However, it is noted that there are fewer 

tests results to validate this conclusion as compared to normalweight 

concrete. Alternatively, for composite components that use 

lightweight concrete, either Proposal 4 of Table 7 should also be 

checked, or the provisions of ACI 318-08 Appendix D or similar 

should be used in total. 

8. Seismic behavior of steel anchors in shear 

Results from the literature generally show that push-out specimens 

having headed steel stud anchors subjected to cyclic shear 

force exhibited lower strength and ductility than corresponding 

monotonic push specimens. A number of experiments on headed 

steel anchors subjected to cyclic loading have been conducted to 

study the behavior of steel frames with reinforced concrete infills. 

For example, Makino [58] conducted experiments were performed 

on single-story, single-bay steel frames with reinforced concrete 

infills at approximately a one-third scale. They estimated that the 

cyclic strength of the studs was approximately 50% of the predicted 

strength from the formulas of Ollgaard et al. [15]. Civjan 

and Singh [38] conducted seven cyclic tests and concluded that 

reversed cyclic loading resulted in nearly a 40% reduction in the 

stud shear strength compared to monotonic strengths computed 

by AISC 2005, attributing this reduction to low-cycle fatigue of 

the stud and weld materials as well as concrete degradation. Gattesco 

and Giuriani [35] tested two specimens under cyclic loading 

and concluded that the accumulated damage during cycles reduced 

the measured monotonic strength by almost 10%. Saari et al. [39] 

carried out eight tests under different combinations of shear and 

tension loads and both monotonic and cyclic loads with different 

amounts of confining reinforcement around the anchors within 

a specimen modeling an infill wall. From their tests they determined 

that when good detailing is provided surrounding the studs 

in the specimen, the cyclic failure always occurred in the steel. Also, 

under shear forces, a 21% reduction in measured monotonic stud 

shear strength was found. 

These reduction factors for cyclic loading (ξ) for conditions representing 

either infill wall specimens or composite slabs without


a b 

c d 

e 

Table 10 

Cyclic shear strength of headed studs. 

Fig. 6. Comparison between steel (0.65AsFu) and concrete predictions with resistance factors and type of failure. 

Code ξ Reference ξ 

AISC 341-05 [31] 0.75 Makino (1984) [58] 0.50 

ACI 318-08 [2] b 

0.75 Civjan and Singh (2003) [38] 0.60 a , b 

NEHRP (2004) [59] 0.75 Gattesco and Giuriani (1996) [35] 0.90 a 

a Failure of the steel. 

b Failure of the concrete. 

Saari et al. (2004) [39] 0.79 a 

metal decking are summarized in Table 10, along with the values 

assumed in several design provisions. While there is variation in 

the recommendations (for example, ACI 318-08 does not require a 

reduction for cyclic loading on the shear strength of steel anchors), 

it may generally be concluded that the 25% reduction in monotonic 

shear strength to account for cyclic loading is reasonable so long as 

the monotonic shear strength is predicted within reasonable statistical 

accuracy. For example, a reduction factor of 0.75 is appropriate 

when used in conjunction with a Cv coefficient or resistance factor 

of 0.65 applied to the nominal shear strength AsFu of a headed stud 

anchor with hef /d ratios larger than 4.5. 

9. Conclusions 

In this work, limit state formulas for headed stud anchors in 

shear specifically in composite construction have been assessed 

versus 391 monotonic and cyclic experiments from the literature 

within the context of the AISC Specification [30,31] and EC-4 (2004) 

[32], and comparisons have been made to the provisions in the 

ACI 318-08 Building Code [2] and the PCI Handbook, 6th Edition [6]. 

New formulas are proposed to predict concrete failure and existing 

formulas for steel failure are evaluated based upon the comprehensive 

experimental data set. The experimental results are 

disaggregated to highlight tests that failed in the steel shank or 

weld, tests that failed in the concrete, or tests that are identified as 

having mixed failure. The scope of this research includes composite 

beam–columns [typically concrete-encased steel shapes (SRCs) or 

concrete-filled steel tubes (CFTs)], concrete-encased and concretefilled 

beams, boundary elements of composite wall systems, composite 

connections, composite column base conditions, and related 

forms of composite construction; composite beams consisting of 

steel girders with composite lightweight concrete slab (with decking) 

are out of the scope of this work. Several conclusions can be 

drawn from this work.

• The most likely concrete failure mode in composite construction 

is pryout failure, rather than breakout failure (with these 

failure modes being as described in ACI 318-08) since there 

are not appropriate failure planes for front-edge or side-edge 

breakout in the majority of composite structures. In this work, 

the concrete breakout strength is deemed not to be a governing 

limit state; such conditions are thus beyond the scope of this 

work. 

• The AISC [30] formula for predicting the steel failure mode in 

headed stud anchors (AsFu) is accurate for steel failures in anchors 

only if a resistance factor is included to ensure an acceptable 

level of reliability, comparable to what is used in PCI 6th 

Edition and ACI 318-08. A resistance factor of 0.65 provides a reliability 

index β of approximately 4. Alternatively, a resistance 

factor of 1.0 may be used if a reduction factor such as 0.65 is 

applied to AsFu. 

• EC-4 (2004) provides conservative results in most cases for steel 

and concrete failures when resistance factors are applied. 

• PCI 6th Edition and ACI 318-08 provide more conservative prediction 

for concrete failures than AISC 2005, with PCI 6th Edition 

being the most accurate. AISC 2005 is generally unconservative 

when anchors fail in the concrete. 

• A selection of formulas to estimate pryout concrete failures are 

proposed as an alternative to the current prediction of concrete 

failure in AISC 2005. The choice of formula is dependent on 

which types of parameters are deemed appropriate to govern 

the concrete failure strength. 

• After assessing the literature regarding headed studs subjected 

to shear, it was deemed that the steel strength formula AsFu with 

a resistance factor equal to 0.65 is the only formula that needs 

to be checked for headed stud anchors that are not subject to 

breakout failures in the concrete, if normal-weight concrete is 

used and if the effective height-to-depth ratio hef /d is larger 

than 4.5 (where hef is measured to the underside of the stud 

head; a comparable minimum value of h/d is 5, where h is the 

total height of the stud). For the few experiments in this category 

that fail in the concrete, the steel strength formula proved 

to be conservative. For composite components with lightweight 

concrete, a larger minimum value of the anchor height is recommended 

because there is less data available for these longer 

lengths, and what data is available shows that the failure tends 

to occur more in the concrete than for normal-weight concrete 

if hef /d is just above 4.5. Based on the limited data available to 

date, a value of hef /d > 6.5 (or a comparable value of h/d > 7) 

more clearly assures that failure will occur in the steel, and thus 

this value is recommended for lightweight concrete if only a 

steel strength formula is to be checked. Additional test results 

could validate using a lower value of this minimum ratio in future 

research. 

• A reduction factor of 0.75 is adequate to design headed stud anchors 

in shear subjected to seismic loads, so long as the monotonic 

steel strength of headed studs has a resistance factor on 

AsFu that is in the range of the values proposed in this work. 

Acknowledgements 

Funding for this research was provided by the Fundación Caja 

Madrid and the University of Illinois at Urbana-Champaign. The authors 

thank Mr. N. Anderson, Dr. D. Meinheit, and Dr. K. Rasmussen 

for sharing their collected data and Mr. M. Denavit of the University 

of Illinois at Urbana-Champaign for his contributions to this 

work. The authors thank the members of the American Institute of 

Steel Construction Committee on Specifications Task Committee 5 

on Composite Construction for their comments on this research. 


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